Understanding GDP Shrinkage and Exponential Decay

The video tutorial explains how the GDP of a country is shrinking by 1.9% per year, starting from 750 billion dollars in 2020. It introduces the concept of exponential decay, which is used to model the GDP over time. The function a(T) = 750 * (1 - 0.019)^T is derived to represent the GDP in billions of dollars T years after 2020, with 0.019 being the decimal form of the 1.9% decay rate.

What is the initial GDP of the country in 2020?

• 900 billion dollars

• 1 trillion dollars

• 750 billion dollars

• 500 billion dollars

What does it mean when a quantity is shrinking by a constant percentage?

• It is undergoing linear decay.

• It is undergoing exponential decay.

• It is undergoing exponential growth.

• It is undergoing linear growth.

Which of the following best describes exponential decay?

• A constant percentage is subtracted each year.

• A constant amount is added each year.

• A constant percentage is added each year.

• A constant amount is subtracted each year.

What is the decay rate expressed as a decimal for a 1.9% decrease?

• 0.019

• 0.19

• 1.9

• 0.0019

Which of the following is the correct formula for the GDP model described?

• a(T) = 750 * (1 + 0.019)^T

• a(T) = 750 * (1 - 0.019)^T

• a(T) = 750 * (1 + 0.19)^T

• a(T) = 750 * (1 - 0.19)^T